For the neural network we implemented an architecture with 4 hidden layers of size \(5|V|\) , \(2|V|\) , \(|V|\)  and \(|V|//2\)  for the WVCP and 9 hidden layers of size \(10|V|\) , \(5|V|\) , \(2|V|\) , \(2|V|\) , \(2|V|\) , \(2|V|\) , \(2|V|\) , \(|V|\)  and \(|V|//2\)  for the \(k\) -COL problem. The neural network is trained at each generation with Adam optimizer [1]} and initial learning rate \(l_r=0.001\) .
